# Math Help - Opposite Travel Direction Problem

1. ## Opposite Travel Direction Problem

Hi there,

I am having a problem creating an equation that would me the correct value for X. It is as follows:

Bob leaves on his bike, traveling north. At the same time, Sue leaves by car, traveling south. Bob and Sue leave from the same location. After 30 minutes, they are 35km apart. Suppose that x represents Bob's speed and (2x + 10) represents Sue's speed, both in kph. Find the speeds at which Bob and Sue travel.

If anyone has any suggestions, I'd appreciate it.

2. ## Re: Opposite Travel Direction Problem

How far apart were they to start?

3. ## Re: Opposite Travel Direction Problem

Originally Posted by SlipEternal
How far apart were they to start?

Sorry, forgot to mention, they started at the same location. Ill revise the first post to reflect that. Thanks.

4. ## Re: Opposite Travel Direction Problem

Ok, so, every hour, Bob travels x km and Sue travels 2x+10 km. That means in half an hour, Bob travels $\dfrac{1}{2}x$ km and Sue travels $\dfrac{1}{2}(2x+10) = x+5$ km. So, add those two distances together. You are told that the sum of those distances is 35 km. This will give you an equation.

5. ## Re: Opposite Travel Direction Problem

I am a bit confused as to how to solve that equation then. I am to determine speed of travel (km/ per hour). I don't know how to find their individual KM in distances without that. How would I proceed to solve for X/speed? My process of eliminations of the above: 1/2 (2x + 10) = x + 5

... just ends up up in a mirror match of 2x + 10 = 2x + 10 and I cannot solve for x.

6. ## Re: Opposite Travel Direction Problem

Hello, Joe222!

Bob leaves on his bike, traveling north.
At the same time, Sue leaves by car, traveling south.
Bob and Sue leave from the same location.
After 30 minutes, they are 35km apart.

Suppose that $x$ represents Bob's speed
. . and $(2x + 10)$ represents Sue's speed, both in kph.

Find the speeds at which Bob and Sue travel.

Making a sketch usually helps . . .
I'll draw it east-to-west to save space.

Code:
      B . . . . . . . 35  . . . . . . . S
* ←---------- * ----------------→ *
: . . x/2 . . O . . (2x+10)/2 . . :
Bob and Sue start at point $O.$

Bob rides west at $x$ kph for $\tfrac{1}{2}$ hour to point $B.$.
. . $OB = \tfrac{1}{2}x$ km.

Sue drives east at $2x+10$ km for $\tfrac{1}{2}$ hour to point $S.$
. . $OS \,=\,\tfrac{1}{2}(2x+10)$ km.

At that time, they are 35 km apart.

. $\tfrac{1}{2}x + \tfrac{1}{2}(2x+10) \:=\:35$

7. ## Re: Opposite Travel Direction Problem

Oh I see now. I have this bad habit of over-complicating things on my end and I miss out on the simple things. I need to work on my perception just a little bit.

Thank you very much for the clarification Soroban. And SlipEternal, thank you very much for explaining it as well; I don't know why I did not put 2 and 2 together.